What involvement of a gentile in the baking determines the bread to be pas akum:
The Sages only forbade gentile baked bread in the event that the baking process was completely done by the gentile. If however a Jew was involved in some part of the baking process then the bread is permitted even though majority of its work was performed by the gentile, and it does not have the Halachic status of Pas Akum. Nevertheless, not all activities that a Jew performs in the baking process have the ability to permit the bread, and only the selected activities which the Sages chose have this power. The selected activities are any one of the following three activities: Entering the dough into the oven; or turning on the flame; or raising the flame. These activities help to permit even bread baked by a gentile homeowner [Pas Baal Habayis], and not just commercially baked gentile bread [Pas Paltar]. [It does not help to perform any other activity within the baking process, and hence even if a Jew made the entire dough, it is forbidden to be eaten if none of the above three activities were performed.] The following are the details of the activities selected by the Sages:
- Entering the dough into the oven: If a Jew entered the dough into the oven, the bread is valid even if [the dough was made by a gentile and] the gentile lit the flame of the oven.
- Lighting the flame: If a Jew lit the flame of the oven, the bread is valid even if [the dough was made by the gentile and] the dough was entered into the oven by the gentile. [So long as this original flame that was lit by a Jew remains lit, a gentile may enter the dough into the oven, even if many days have passed.]
- Raising the flame: If a Jew raised the flame of the oven to a higher temperature, the bread is valid even if a Gentile lit the flame of the oven and [made the dough and] entered the bread into the oven. The raising of the flame helps to validate the bread even if the dough was already placed into the lit oven by the gentile and it already began baking to the point that it browned, so long as the bread still needs to remain in the oven and the further baking of the bread is still of benefit to it.
The bread was baked without any of the above activities performed: If the bread was already baked by the gentile and removed from the oven without any of the above activities being performed by the Jew, then some Poskim rule that if further baking will be of benefit to the bread, then a Jew may permit the bread by returning it to the oven for the further baking. [Practically, we do not rule like this opinion, even Bedieved.]
 112/9; Avoda Zara 38b
 The reason: The reason for why the Sages allowed these activities to permit the bread is because these activities serve as a recognition [Heker] that one may not eat Pas Akum [and come to intermingle with the gentiles and intermarry]. [Michaber ibid]
 Kisei Eliyahu 112/5; Peri Chadash 112/1; Birkeiy Yosef 112/18; Kaf Hachaim 112/51
 The Michaber ibid states as follows “If one stoked the flame even slightly, it is permitted. Even if he only threw one piece of wood into the oven, he has validated all of the bread that is in it” The Rama ibid [based on Iggur; Tur; Maharil 221] adds that “If he blew at the flame it is considered as if he stoked it” The above was only applicable in previous times that the baking was performed through wood fuel. Today however in which we use gas flames or electric, the equivalent of the above is simply raisning the knob of the flame or raising the temperature. [See Sefer Hakashrus 19/7]
 Michaber 112/9
 Michaber 112/12; Mordechai chapter 2 of Avod Zara
 Michaber 112/12
 Opinion in Michaber 112/12; Iggur in name of Shaareiy Dura
 Kaf Hachaim 112/63 based on Klalei Michbaer as brought in Machazik Bracha 9/2; Zivcheiy Tzedek 112/38